1. Field of the Invention
The present invention broadly pertains to systems for testing physical structures using modal analysis. The invention more particularly concerns a system for ascertaining the dynamic or vibrational behavior of a structure by means of directional microwave signals which emanate from the structure in a variable manner, representing forces applied to the structure. Oscillators located on a sensor mounted on the structure generate the signals which have separate frequencies and generally common directions. Movements of the oscillators cause movements of the signals which are detected by remote receivers positioned in line of sight relation with the structure-under-test.
2. Related Art
Modal analysis in general terms is a system of testing structures to obtain a mathematical description of their dynamic or vibrational behavior. A structure undergoing such an analysis is referred to herein as a structure-under-test. A resulting mathematical description will typically include such behavioral data as the structure's natural frequencies (the frequencies when no external force is applied), damping factors, and mode shapes (relative deformations as a function of frequency). These data are typically represented as matrices which are, in turn, expressed as eigenvectors and eigenvalues.
Complex algebra (with real and imaginary components) is commonly used to describe both magnitude and phase information of a structure-under-test. More specifically, an imaginary number represents a value in a plane that is perpendicular to the plane in which a measurement is being taken. Thus, in modal testing, imaginary numbers represent measurements of an out-of-plane component of a vibration. This measurement of various vibration modes by modal testing is used to compare measured data with corresponding data produced by a theoretical model. Commonly, the theoretical model used is a finite element model.
Presently, in modal analysis, engineers attach accelerometers to several points along a structure-under-test. The structure-under-test is then subjected to a known force or vibration. The accelerometers generate responses to the force or vibration. These responses are recorded. In many experiments, mobility is the parameter of interest. Mobility is calculated by dividing velocity by the force applied to the structure-under-test. To determine mobility, the accelerometers are connected to electronic integrators which convert measured acceleration into velocities. These integrators are resistive-capacitive circuits which act as low-pass filters. Using a Fast Fourier Transform to obtain frequency response functions, measured data in a time domain are converted into data in a frequency domain.
Once frequency response data are recorded, natural frequencies, mode shape matrices, and damping factors can be derived mathematically. One of the most common methods for effecting such mathematical derivations is the circle-fit method. This method uses Nyquist circle plots of frequency response data. A Nyquist circle is a plot of real and imaginary components of frequency response data--these real and imaginary components tend to form a circle. The circle-fit method works because, in the vicinity of most systems' resonance, vibrational behavior is dominated by a single mode. By measuring the maximum rate of change of the frequencies along the circle, the natural frequency and damping factors may be found. The amount of error for such a natural frequency measurement is typically plus or minus 10%. The Nyquist plot uses the data obtained by the accelerometers from a structure that was subjected to a known force. The circle-fit method then allows determination of the structure's natural frequency and damping factors. Once natural frequency and damping factors are known, the modal constant and a mode shape matrix may be derived.
Almost all modal analysis has required use of piezoelectric or piezoresistive accelerometers. As is well-known, accelerometers measure dynamic responses. However, piezoelectric and piezoresistive accelerometers for modal analysis have certain limitations. For example, accelerometers can only measure linear acceleration in one direction. To measure acceleration in three directions, three mutually perpendicular accelerometers are bound together. Each individual signal is then matched in time and phase to deduce true three-dimensional movement of the structure-under-test. The imaginary component (the complex mode) for each accelerometer is then mathematically transformed into real normal modes by a known matrix manipulation technique. The higher the frequency of the vibration being measured, the more difficult it is to match all three signals. Moreover, a single piezoelectric or piezoresistive accelerometer cannot directly measure rotation in more than one plane. Accordingly, rotation has been deduced by comparing the signals of two or more closely spaced accelerometers on a structure-under-test. Additionally, some accelerometers currently in use have limited dynamic ranges. Thus, structures subjected to a wide range of forces may require one set of accelerometers to measure low accelerations, such as 5 g's, as well as a second set of accelerometers to measure high accelerations, such as 100 g's. Further, most piezoelectric and piezoresistive devices cannot measure true static conditions; they can only reliably measure changes in acceleration. Only variable capacitance accelerometers such as Endevco's Microtron can measure low-level accelerations in a steady-state or low-frequency environment.
The physical chemistry, design, and construction of piezoelectric and piezoresistive accelerometers have also resulted in certain limitations; namely, limitations in the accuracy of signals produced by the devices. More specifically, piezoelectric crystals subjected to large dynamic forces may produce electrical outputs sufficient to temporarily or even permanently reduce the sensitivity of the crystals. Signals from piezoelectric crystals may also be affected by drift and a circuit's time constant, thereby producing an undesirable change in output signal over time which is not a function of the measured variable. Typically an amplified signal may either drift towards a saturation level defined by the power supply, or it may decay towards zero at the time constant rate.
Piezoresistive systems are also affected by vibration rectification, that is, that a DC output of such an accelerometer changes as a function of vibration level. This means that when vibrations are being measured, an anomalous DC offset may occur. The main reason for vibration rectification is a simple DC scaling nonlinearity of the basic accelerometer response, although asymmetric damping of an accelerometer's seismic mass may also be a contributing factor.
It is also known that both piezoresistive and piezoelectric devices must be constructed carefully so that no built-in stresses are present which can affect the performance of an instrument in which the accelerometer is contained.
Most known related art systems use piezoelectric or piezoresistive devices. Accordingly, most related art systems can only measure acceleration normal to the plane on which the devices are attached, and they cannot directly measure rotation. Most known systems measure rotational response by recording the outputs of at least two closely spaced accelerometers, and then computing the mean and difference of their outputs. Unfortunately, with these systems, measurement of rotational frequency response functions commonly requires acquisition and processing of several different measurements. Some rotational accelerometers and shakers have been specially developed, but these produce poor results because prevailing levels of output signals generated by translational components of a structure's movement tend to overshadow any output signals due to rotational motions.
A piezoelectric and piezoresistive transducer element has been described in the art which employs a pair of electromechanically reacting, oscillating beams affixed to a main axis which is attached to a base plate. This device is stated to measure angular acceleration parallel to the surface on which it is affixed as well as linear acceleration normal to that surface. This device, however, can only measure linear acceleration in one direction and angular acceleration in another direction; consequently, three of these devices must be attached in mutually perpendicular directions in order to measure true three-dimensional movement.
Another suggested device utilizes laser beam interferometers for detecting displacements of points of an excited structure. Once again, a plurality of these devices is necessary to determine three-dimensional movements of the structure. If the structure is vibrating rapidly, the point that is being measured by the interferometers can change with the structure's vibration--i.e., the structure's vibrations can prevent the laser beams from remaining focused on a single point.
Still another suggested device uses Doppler signals from two parallel laser beams to measure rotational velocity of a body and, hence, the rotational vibration or vibrations of that body in the same direction as the laser beams.